PSI - Issue 2_A

F.De Cola et al. / Procedia Structural Integrity 2 (2016) 2905–2912 Author name / Structural Integrity Procedia 00 (2016) 000–000

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of December 2014. Two types of confinements were designed in order to characterize the granular assemblies under uniaxial strain and uniaxial stress loading conditions. A stiff titanium alloy cylindrical confinement was used to reproduce uniaxial strain loading conditions whilst a compliant latex one was used to reproduce uniaxial stress conditions. Sand samples of mass correspondent to the representative volume element were defined by means of a high precision weighing scale and subsequently compacted using a specimen filling procedure established to obtain experimentally fixed and reproducible void ratios.

Nomenclature e

void ratio porosity

n

V v V s

volume of voids volume of solids

V tot

total volume available

dimension of the fictitious volume diameter of the real container

d

D L n p

length of the sample in the loading direction number of particles in the assembly history of the incident strain signal history of the reflected strain signal

ε i ( t ) ε r ( t ) ε t ( t )

history of the transmitted strain signal A 0 , A s cross sectional area of bars and specimen E 0 , C 0 Young’s modulus and elastic wave speed of the bars radius of

2. Computation of the void ratio within the sample The definition of the RVE takes into account the variation of relative density within the granular assembly. A series of three dimensional simulations were conducted using an in-house developed software (DEST – Discrete Elements Simulation Tools) in order to simulate the statistically representative distributions of sand grains which were expected to be generated during specimen preparation and predict their consolidation states within the samples volume. The boundary conditions imposed by the lateral walls of the confinement influence the distribution of grains in the sand assembly. Their distribution appears ordered in proximity of the walls whilst particles located far from the walls are disposed in a casual manner. Consequently particles within a distance of 2-4 equivalent particle diameters have shown not to be statistically representative of the consolidation of the granular media (Blumenfeld et al. (2005), Landry et al. (2003), Man et al. (2005)). The hereby proposed numerical procedure allows for the prediction of the relative packing density obtained during diverse deposition processes and is applicable to different granular materials. Rewriting equation (1) it is possible to express the void ratio as a function of the total volume V tot of a generic container and the volume V s of the particles, or fraction of particles, enclosed in it. ݁ ൌ ௏ ೡ ௏ ೞ ൌ ௏ ೟೚೟ ି௏ ೞ ௏ ೞ ൌ ௏ ೟೚೟ ௏ ೞ െ ͳ (4) The proposed numerical procedure computes the volume V tot of a sequence of virtual boxes of dimension ( d ) smaller than the dimension ( D ) of the real sample as a whole (Fig 1) and the volume V s of solids enclosed in them. The volume of fraction of particles is taken into account and it is determined using different geometry relations dependent on the relative position between particles and boundary (De Cola et al., (2016)). By incrementing simultaneously the dimensions of these virtual volumes starting from the geometrical center of the sample, it is possible to define how the void ratio varies across the specimen.